Your host at a party has decided to play

an obscure game. He paints all his guests' foreheads so that they

can all see the color in each other's face but don't know their own. Once he

finishes painting everybody's forehead, the host informs them that that

everyone has been painted with either red or blue paint, and that there's

at least one person's forehead painted blue. The game will have multiple rounds.

The guests are to enter a dark room and sit down forming a circle. The light

will then be is switched on, allowing everybody to take a look around but no

communication will be allowed. Then, the light will be switched off again and

if anyone has somehow figured out he has a blue forehead, he or she must

leave the room. This will continue until there's nobody with a blue forehead

left in the room. 

Now picture this scenario: what if all 20 people have been

painted a blue forehead? Assuming they all have a

perfectly logical mind, how would the game go?